This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. Asplund, Comparison between plane symmetric convex bodies and parallelograms, Math. Scand. 8 (1960), 171–180.
J. Bourgain and V.D. Milman, Distances between normed spaces, their subspaces and quotients spaces, Int. Eq. and Oper. Th. 9 (1986), 31–46.
J. Bourgain and S.J. Szarek, The Banach-Mazur distance to the cube and the Dvoretzky-Rogers factorization, Israel J. Math. 62 (1988), 169–180.
J. Bourgain and L. Tzafriri, Invertibility of “large” submatrices with applications to the geometry of Banach spaces and harmonic analysis, Israel J. Math. 57 (1987), 137–224.
A. Dvoretzky and C.A. Rogers, Absolute and unconditional convergence in normed linear spaces, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 192–197.
E.D. Gluskin, The diameter of the Minkowski compactum is roughly equal to n, Funct. Anal. Appl. 15 (1981), 72–77.
Y. Gordon, Some inequalities for Gaussian processes and applications, Israel J. Math. 50 (1985), 265–289.
_____, On Milman’s inequality and random subspaces which escape through a mesh in ℝn, GAFA, Israel Functional Analysis Seminar (86/87), Springer, LNM 1317 (1988), 84–106.
F. John, Extremum problems with inequalities as subsidiary conditions, in “Courant Anniversary Volume”, Interscience, New York, 1948, 187–204.
B.S. Kashin, Some properties of matrices of bounded operators from ℓ m2 into ℓ m2 , Izv. AN Armyanskoi SSR 5 (1980), 379–394.
H. König and N. Tomczak-Jaegermann, Bounds for projection constants and 1-summing norms, Trans. AMS 320 (1990), 799–823.
A. Lubotzky, R. Phillips and P. Sarnak, Ramanujan graphs, Combinatorica 8 (1988), 261–277.
V.D. Milman and G. Schechtman, “Asymptotic Theory of Finite Dimensional Normed Spaces”, Lecture Notes in Math. v.1200, Springer-Verlag.
A. Pełczyński, Structural theory of Banach spaces and its interplay with analysis and probability, in “Proceedings of the ICM 1983”, PWN — North Holland, 1984, 237–269.
N. Sauer, On the density of families of sets, J. Comb. Theory Ser.A 13 (1972), 145–147.
S. Shelah, A combinatorial problem: stability and order for models and theories in infinitary languages, Pacific J. Math. 41 (1972), 247–261.
S.J. Szarek, Spaces with large distance to ℓ m∞ and random matrices, Amer. J. Math. 112 (1990), 899–942.
_____, Condition number of random matrices, J. of Complexity, to appear.
S.J. Szarek and M. Talagrand, An “isomorphic” version of the Sauer-Shelah lemma and the Banach-Mazur distance to the cube, GAFA-Israel Funct. Anal. Sem. (J. Lindenstrauss, V.D. Milman, eds.), Lecture Notes in Math., v.1376, Springer-Verlag, 105–112.
N. Tomczak-Jaegermann, “Banach-Mazur Distance and Finite Dimensional Operator Ideals”, Longman, 1988.
D. Voiculescu, Property T and approximation of operators, Bull. London Math. Soc. 22 (1990), 25–30.
E. Wigner, Characteristic vectors of bordered matrices with infinite dimension, Ann. of Math. 62 (1955), 548–564.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag
About this paper
Cite this paper
Szarek, S.J. (1991). On the geometry of the Banach-Mazur compactum. In: Odwell, E.E., Rosenthal, H.P. (eds) Functional Analysis. Lecture Notes in Mathematics, vol 1470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090211
Download citation
DOI: https://doi.org/10.1007/BFb0090211
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54206-3
Online ISBN: 978-3-540-47493-7
eBook Packages: Springer Book Archive